Noise-to-State Stability for Stochastic Hopfield Neural Networks with Delays∗

It is well known that stability of Hopfield type neural networks plays a very important role in both theoretical research and applications. So, it has been kept on studying in two decades. Stochastic effectiveness to this kind of neural networks has also received a lot of attention (ref. [Liao et al, 1996 A], [Liao et al, 1996 B], [Blythe,S. et al, 2001A] and [Blythe,S. et al, 2001B]). In this paper, we intend to present some new results on robust noise-to-state stability of delayed Hopfield neural network via Razumikhin technique. Our motivation is based on the intention to discover the effect of uncertain stochastic noise to the state of the neural networks. An example shows the kind of stability could be used to design a kind of Hopfield neural networks described by cascade stochastic systems to implement associative memory.